The following scores were obtained by 11 footballers in a goal-competition 536878311632. The median score was?

The inverse of f is a function which takes any value x and divides it by 4, then adds 7 to the result.

The inverse of a function is the opposite of the original function, meaning that it takes the output of the original function and turns it back into the input. In this case, the original function is f(x)=1/4x+7. To find the inverse, we need to solve for x in the equation, which can be done by subtracting 7 from both sides and then multiplying both sides by 4. This gives us x=(x+7)/4, which is the inverse of the original function. To put it simply, the inverse of f takes any output of the original function, adds 7 to it, and then divides it by 4 to get the original input.

example;

If f(x)=1/4x+7 and x=3, then

f(3) = (1/4)3 + 7

7.75

The inverse of f is f^-1(x) = (x + 7) / 4.

If f^-1(7.75) = (7.75 + 7) / 4, then

f^-1(7.75) = 14.75 / 4

3.6875

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y = 2/3x - 1

It will be Option 2.

The value of m so that the condition satisfies is -2, the correct option is A.

We are given that;

y=f(x) is continuous

Now,

To find the numbers c that satisfy the conclusion of the Mean Value Theorem, we need to solve the equation:

f’© = [f(2) - f(0)] / (2 - 0)

f’(x) = 8x - 2

f(2) = 4(2)^2 - 2(2) + 3 = 23

f(0) = 4(0)^2 - 2(0) + 3 = 3

f’© = (23 - 3) / (2 - 0)

f’© = 10

8m - 2 = 10

8m = 12

m = 12/8

m = -2

Therefore, by the given function the answer will be -2.

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The value of the pressure is 1 when the value of volume is 10 liters, the correct option is D.

Pressure is defined as the physical force exerted on an object.

The force applied is perpendicular to the surface of objects per unit area.

Given

The equation is

\(\rm V=\dfrac{10}{p}\)

Where the v is the volume and p is the pressure.

The value of p when the value of volume v is 10 liters is;

\(\rm V=\dfrac{10}{p}\\\\\rm 10=\dfrac{10}{p}\\\\P = \dfrac{10}{10}\\\\P=1\)

Hence, the value of the pressure is 1.

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Answer:

1/2

Step-by-step explanation:

12 / 24 = 1/2

Answer:

12/24

Step-by-step explanation:

use the stander rise over run since the rise is 12 it goes over the run which is 24

To show that the expression ((P1 V P2 V P3) ^ (P1 → q) ^ (P2 → g) ^ (P3 → q)) → q is a tautology, we can use logical equivalences and logical rules. Let's break down the proof step by step:

Start with the given expression: ((P1 V P2 V P3) ^ (P1 → q) ^ (P2 → g) ^ (P3 → q)) → q

Apply the implication rule: ¬(P1 V P2 V P3) V q

Apply De Morgan's law: (¬P1 ∧ ¬P2 ∧ ¬P3) V q

Use the logical equivalence ¬(A ∧ B) ≡ ¬A ∨ ¬B: (¬P1 V q) ∧ (¬P2 V q) ∧ (¬P3 V q)

Apply the implication rule to each subexpression: (P1 → q) ∧ (P2 → q) ∧ (P3 → q)

Apply the logical equivalence A ∧ B ≡ B ∧ A: (P1 → q) ∧ (P2 → q) ∧ (P3 → q)

Apply the logical equivalence A ∧ (B ∧ C) ≡ (A ∧ B) ∧ C: ((P1 → q) ∧ (P2 → q)) ∧ (P3 → q)

Apply the logical equivalence A → (B → C) ≡ (A ∧ B) → C: ((P1 → q) ∧ (P2 → q)) → (P3 → q)

Apply the logical equivalence (A → B) → C ≡ A → (B → C): (P1 → (P2 → q)) → (P3 → q)

Apply the logical equivalence A → (B → C) ≡ ¬B → (A → C): ¬P2 → ((P1 → q) → (P3 → q))

Apply the logical equivalence A → (B → C) ≡ (A ∧ B) → C: (¬P2 ∧ (P1 → q)) → (P3 → q)

Apply Modus Ponens: (P1 → q) → (P3 → q)

Apply the logical equivalence A → A: A → A

Apply the logical equivalence A → (B → A): (P3 → q) → (P3 → q)

Apply Modus Ponens: P3 → q

Apply Modus Ponens: (¬P2 ∧ (P1 → q)) → q

Apply Modus Ponens: ((P1 → q) ∧ (P2 → q)) → q

Apply Modus Ponens: (P1 → q) → q

Apply Modus Ponens: ((P1 V P2 V P3) ^ (P1 → q) ^ (P2 → q)) → q

Apply Modus Ponens: ((P1 V P2 V P3) ^ (P1 → q) ^ (P2 → q) ^ (P3 → q)) → q

By applying logical equivalences and logical rules, we have shown that the expression ((P1 V P2 V P3) ^ (P1 → q) ^ (P2 → q) ^ (P3 → q)) → q is a tautology.

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Answer:

1/5

rise over run

1- the inches

over 5- the days

The correct answer is approximately 86.67% of adults surveyed drink either coffee or tea.

To determine the percentage of adults who drink either coffee or tea, we need to add the number of adults who drink coffee and the number of adults who drink tea and subtract the number of adults who drink both.

Number of adults who drink either coffee or tea = Number of adults who drink coffee + Number of adults who drink tea - Number of adults who drink both

= 50 + 30 - 15

= 65

Out of the total 75 people surveyed, 65 adults drink either coffee or tea. To find the percentage, we divide the number of adults who drink either coffee or tea by the total number of adults surveyed and multiply by 100.

Percentage of adults who drink either coffee or tea = (65 / 75) * 100

≈ 86.67%

Therefore, approximately 86.67% of adults surveyed drink either coffee or tea.

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The derivative of the function y = x^2x using logarithmic differentiation is dy/dx = x^2x(2 + 2ln(x)).

To find the derivative of the function y = x^2x using logarithmic differentiation, we follow these steps:

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To find the derivative of the function y = x^(2x) using logarithmic differentiation, we take the natural logarithm of both sides, apply logarithmic properties, and then differentiate implicitly.

Start by taking the natural logarithm of both sides of the equation:

ln(y) = ln(x^(2x))

Apply the power rule of logarithms to simplify the expression:

ln(y) = 2x * ln(x)

Now, differentiate both sides of the equation implicitly with respect to x:

(1/y) * dy/dx = 2 * ln(x) + 2x * (1/x)

Simplify the expression:

(1/y) * dy/dx = 2 * ln(x) + 2

Multiply both sides by y to isolate dy/dx:

dy/dx = y * (2 * ln(x) + 2)

Substitute the original value of y = x^(2x) back into the equation:

dy/dx = x^(2x) * (2 * ln(x) + 2)

The derivative of the function y = x^(2x) using logarithmic differentiation is dy/dx = x^(2x) * (2 * ln(x) + 2). Logarithmic differentiation is a useful technique for differentiating functions that involve exponentials or complicated algebraic expressions, as it allows us to simplify the calculation by taking the logarithm of both sides and then differentiating implicitly.

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Answer: 0.84

16/19 = 0.8421....

0.8421 rounded to the nearest tenth is 0.84.

The answer is 0.84.

Answer: 56 inches

Step-by-step explanation:

a. 60+58+64+72=254 (Add the average of his family without including him)

a. 62x5=310 (The average times 5, cause there are 5 of them will get you the total number of inches)

b. 310-254=56 (Subtract the total number of the 5 of them with the 4 of them to find Bill's height)

you can check your answer by adding all their heights.

Answer:

V=w*h*l

Step-by-step explanation:

w=width

h=height

l=length

volume = w*h*l

volume = w*h*l

volume = w*h*l

The graph of the proportional relationship y = 6x is given by the image presented at the end of the answer.

The slope of the line is of 6.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

She buys 6 snacks for each student who enrolls, hence the constant is given as follows:

k = 6.

Then the equation is given as follows:

y = 6x.

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Answer:

Here is the result:

(2, 3)      ↔      (2, 2)                     ∵ x = 2 is duplicated

(-5, 2)     ↔      (-5, 1)                     ∵ x = -5 is duplicated

(6, -5)     ↔      (6, 5)                     ∵ x = 6 is duplicated

(-1, 0)      ↔      (-1, 6)                     ∵ x = -1 is duplicated

Here, each matching pair has duplicated input values, so neither of them represents the function.

Step-by-step explanation:

We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.

In other words, we can not have duplicated inputs as there should be only 1 output for each input.

We are given that we need to match the ordered pairs so that the relation defined by the set of ordered pairs does not represent a function.

Therefore, all we need is to match the ordered pairs which have the same input value as it would violate the relation to be function.

Here is the result:

(2, 3)      ↔      (2, 2)                     ∵ x = 2 is duplicated

(-5, 2)     ↔      (-5, 1)                     ∵ x = -5 is duplicated

(6, -5)     ↔      (6, 5)                     ∵ x = 6 is duplicated

(-1, 0)      ↔      (-1, 6)                     ∵ x = -1 is duplicated

Here, each matching pair has duplicated input values, so neither of them represents the function.

Answer:

Step-by-step explanation:

17, is the answer.

Answer:

The answer is terminating!

Step-by-step explanation:

repeating never ends

Answer:

B: terminating.

Step-by-step explanation:

Repeating and terminating are two different types of decimal number.

If a decimal has an end, it can be said to be terminating. 1.255 clearly ends on the last '5', and is therefore terminating.

A repeating decimal is one that never ends. For example, if you were to divide 1 by 3, the answer would be 0.3333333333333333333333... going on forever. You can identify repeating decimals by the dot usually used to represent them: for example, 0.3 with a dot above the 3 is equal to 1/3.

36

that is the answer

Answer:

36%

Step-by-step explanation:

"Percent'' or ''%'' means ''out of 100'' or '' per 100'',

Therefore x% can be written as x/100.

So we can write and solve for x;

27/75= x/100

100 X 27/75 = 100 X x/100

2700/75 = 100 X x/100

36=x

27/75= 36/100= 36%

Hope this helped

At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.

The speed of an object is the ratio of distance and time it takes for the object to travel that distance.

Mathematically,

S = D/T

where

S is velocity

D is the distance traveled or distance traveled

T is the time it takes to travel that distance

Velocity is considered a scalar quantity. A scalar size only has a size. It does not provide information about the direction of object movement.

If an object moves at a constant speed, it means that the object moves the same distance in the same time interval.

Acceleration of an object is the ratio of velocity and time. vector size. Vector quantities have both magnitude and direction.

Mathematics,

a = v/t

When an object is in motion, its acceleration is never zero.

When an object moves, it moves a constant distance over time. Therefore, body positions cannot be the same from the same coordinate system.

Given in the question:

First the plane was travelling at a constant rate of 250  miles per hour.

Initial height was 20000 feet

Now,

As the speed increases and travels at a constant rate of 400 miles per hour.

Now,

   (400 /250 ) × 20000

=  1.6 × 20000

= 32000 feet

Thus, At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.

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Answer:

y= -1

Step-by-step explanation:

the answer is:

y= -1

since it's constant .

La casa está a 37 millas del aeropuerto más cercano.

Utilizando el teorema de Pitágoras, podemos determinar la distancia de la casa al aeropuerto. La distancia horizontal del avión al aeropuerto será la misma que la distancia horizontal de la casa al aeropuerto. Por lo tanto, podemos utilizar el teorema de Pitágoras para encontrar la distancia horizontal:

distancia horizontal al cuadrado + altura al cuadrado = distancia total al cuadrado

distancia horizontal al cuadrado + 5^2 = 42^2

distancia horizontal al cuadrado = 42^2 - 5^2

distancia horizontal = raíz cuadrada de (42^2 - 5^2)

distancia horizontal = raíz cuadrada de (1,739)

distancia horizontal ≈ 41.7 millas

Por lo tanto, la casa está a una distancia horizontal de aproximadamente 41.7 millas del aeropuerto. Para encontrar la distancia total al aeropuerto, agregamos la altura del avión a la altura de la casa:

distancia total = distancia horizontal + altura del avión

distancia total = 41.7 + 5

distancia total ≈ 46.7 millas

Por lo tanto, la casa está a una distancia de aproximadamente 37 millas (46.7 - 5) del aeropuerto.

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Answer:

Step-by-step explanation:

For example, it is more usual to talk about polynomials of degree 6 than to ... Given the polynomials f (x)=3x3 +7x2−5x + 8, g(x) = −x5 + 6x4−2x3+ x−3 ...

Ignatius of Loyola, the Spanish priest and theologian who founded the Society of Jesus (Jesuits) in the 16th century, focused on several key issues during the period of the Counter-Reformation.

These issues can be broadly categorized into spiritual, educational, and institutional reforms.

Spiritual Reforms: Ignatius emphasized the importance of personal piety and spiritual discipline. He promoted the practice of spiritual exercises, including meditation, prayer, and self-examination, to cultivate a deep and intimate relationship with God. Ignatius encouraged individuals to reflect on their sins and seek forgiveness through confession and penance.

Educational Reforms: Ignatius recognized the power of education in shaping individuals and society. He established schools and universities to provide a comprehensive education that combined intellectual rigor with spiritual formation. The Jesuits placed great emphasis on academic excellence, encouraging critical thinking, the pursuit of knowledge, and the integration of faith and reason.

Pastoral Reforms: Ignatius focused on improving the quality of pastoral care and religious instruction. He trained his followers to be skilled preachers and spiritual directors, equipping them to guide and support individuals in their spiritual journey. Ignatius also emphasized the importance of catechesis, ensuring that people received proper religious education and understood the teachings of the Catholic Church.

Missionary Work: Ignatius and the Jesuits had a strong missionary zeal. They undertook extensive missionary endeavors, particularly in newly discovered territories during the Age of Exploration. They sought to bring Christianity to non-Christian lands and convert indigenous populations to Catholicism. The Jesuits established missions, schools, and hospitals in various parts of the world, playing a significant role in spreading Catholicism.

Overall, Ignatius of Loyola's reforms aimed to strengthen and revitalize the Catholic Church in response to the challenges posed by the Protestant Reformation. His focus on personal spirituality, education, pastoral care, and missionary work contributed to the renewal and expansion of the Catholic Church during the Counter-Reformation.

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Answer:  1  1/2

You can write this as 1 & 1/2

The whole part is 1. The fractional part is 1/2

==========================================================

Explanation:

Let's say we had 18 cookies to hand out to 12 students.

How many cookies does each student get?

Using a calculator shows that 18/12 = 1.5 which means they get one whole cookie each

The leftovers is 18-12 = 6

Then notice how 6/12 = 1/2

So that's how the improper fraction 18/12 becomes the mixed number 1 & 1/2

So each student gets 1 full cookie, plus half a cookie.

------------------

Or we could do the problem like this

18/12 = (12+6)/12

18/12 = (12/12)+(6/12)

18/12 = 1 + (1/2)

18/12 = 1 & 1/2

The one mean z test can be used for a sample of moderate size (between 15 and 30) when the population standard deviation is known and the population distribution is approximately normal or the sample size is sufficiently large (n ≥ 30).

When to use the one mean z-test for a sample of moderate size (between 15 and 30).
The one mean z-test is used to compare the sample mean to a known population mean when the population standard deviation is known.

we can use this test for a sample of moderate size (between 15 and 30) under the following conditions:
The population is normally distributed, or the sample size is large enough (usually greater than 30) for the Central Limit Theorem to apply.

However, since your sample size is between 15 and 30, it is crucial that the population is normally distributed.
The population standard deviation is known.

This is essential for calculating the z-score.
The sample is random and independent, meaning each observation in the sample is unrelated to the others.
If these conditions are met, we can use the one mean z-test for a sample of moderate size (between 15 and 30) to test hypotheses about the population mean.

The test will allow you to determine if there is a significant difference between the sample mean and the known population mean.

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Ayana's car was at the shop for 38 minutes for the oil change.

Here we are given that Ayana dropped her car at the shop at 19 minutes to noon for an oil change.

When the time is said with the word "to", it means that we need to subtract the minutes from hours to get the actual time.

Therefore, 19 minutes to noon would be

12 : 00 - 19 minutes

= 11 : 41 a.m

Now, she picked her car up 29 minutes past noon. Since the word past has been used, we need to add up the hours and minutes mentioned hence we get

12 : 00 + 19 minutes

= 12 : 19 p.m

Now we need to find the time the car was at the shop. For this, we will subtract the time the car came in the shop from the time at which the car left the shop.

Hence we get

12 : 19 - 11 : 41

Now clearly, 19 > 41, hence we will carry over 60 mnutes from the hoyrs to get

11 : 79 - 11 : 41

= 38 minutes.

Hence, Ayana's car was at the shop for 38 minutes for the oil change.

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Answer:

66

Step-by-step explanation:

a^5

Answer:

16 929

Step-by-step explanation:

a1 = 22      d = 11     a 54  = 605

Sum = 54 ( 22 + 605) /2 = 16 929  

Doing factorization, we know that the factors of the given equation are ±√5 and ±10i.

In mathematics, factorization or factoring consists of writing a number or any mathematical item as a product of several factors, typically small or easier objects of the same.

For example, 3 × 5 is a factorization of an integer 15 and is a factorization of an equation x² – 4.

So, we have the equation:

x⁴ + 95x² – 500 = 0

Factorizing the above equation:

x⁴ + 100x² - 5x² - 500 = 0

x²(x² + 100) - 5(x² + 100) = 0

(x² - 5)(x² + 100) = 0

Solving further:

x² = 5

x² = -100

x = ±√5

x = √-100

Factors: ±√5 and ±10i

Therefore, doing factorization, we know that the factors of the given equation are ±√5 and ±10i.

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Complete question:
What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.

x=+- sqrt 5 and x = ±10

x=+- sqrt i5 and x = ±10i

x=+- sqrt 5 and x = ±10i

x=+- sqrt i5 and x = ±10

Answer: 80 ft²

Step-by-step explanation:

The area of a trapezoid is one half  the product of the height and the sum of the lengths of the  bases.

(6 + 10) * 0.5 * 10 = 80 (ft²)

The power required for a student to climb a height of 2 meters in 5 seconds, while weighing 400 Newtons, can be calculated.

Power is defined as the rate at which work is done or energy is transferred. To calculate power, we need to determine the amount of work done and divide it by the time taken. In this case, the work done is equal to the product of force and displacement. The force is the weight of the student, which is 400 Newtons, and the displacement is the height climbed, which is 2 meters. The work done would be 400 Newtons multiplied by 2 meters, resulting in 800 Joules. To calculate power, we divide the work done (800 Joules) by the time taken (5 seconds), which gives us a power of 160 Watts. Therefore, the power required for the student to climb a height of 2 meters in 5 seconds is 160 Watts.

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